Magnetic bearings are used in different rotating machines such as electric motors, compressors, turbines, generators, and the like in order to maintain the axial and/or radial positions of a rotating shaft by means of magnetic fields acting on a rotor affixed to the rotating shaft of the rotating machine. Typically, an individual magnetic bearing may include multiple electromagnets disposed about the rotor and utilized to “pull” the rotor in the appropriate direction to maintain the axial and/or radial positions of the rotating shaft. Generally, each electromagnet may include a coil at least partially surrounding a ferromagnetic core. Positive and negative voltages from a power source may be applied to any coil to drive the magnetic flux density up or down and to account for parasitic voltage drops such as cable and coil resistance.
The force exerted by an electromagnet is F=(B2A)/(2u0) where B is the magnetic flux density, A is the magnet area, and u0 is the permeability of free space. It should be noted that force is proportional to the square of the flux density for a single electromagnet. The flux density is changed by the application of voltage to the electromagnet coil for a period of time according to Faraday's law, d(BA)/dt=−VB/N where VB is the voltage applied to change the flux density, t is time, and N is number of wire turns on the coil. Additional voltage must be applied to the coil to overcome the voltage drop due to resistance, VR=IR, where VR is the voltage of the resistive drop, I is the coil current, and R is the total resistance of the coil and cable coupled thereto. The total voltage applied by the amplifier is V=VR+VB. This is best understood by saying that any amplifier voltage not used for the IR drop will be used for changing the flux density, or VB=V−VR.
Accordingly, switching amplifiers may be used in magnetic bearings to apply the voltages from the power source to the coils via one or more cables. Generally, switching amplifiers use switching devices, such as transistors, operated as electronic switches capable of alternating between conductive and nonconductive states. In general, switching amplifiers repeatedly and independently connect lead wires of the electromagnet coil to the positive or negative side of the power source. Switching amplifiers may be highly efficient since the transistors utilized therein are typically either fully on (saturated) or fully off, which minimizes power losses in the transistors. However, although efficient, switching amplifiers may be subject to certain drawbacks, one of which is electromagnetic interference (EMI). EMI may occur when the lead wires of the coil are switched between the positive and negative voltages of the power source at the switching frequency, thereby causing the lead wires to act as an antenna radiating EMI at harmonics of the switching frequency. Switching amplifiers have characteristic rapid change of voltage in a short time that puts significant high-frequency voltages onto the cable. Furthermore the coil lead wires, having self-inductance and stray capacitance between them, may act as transmission lines, causing the cable to resonate at high frequency following every switching event. This resonance may produce voltage transients at the coils that stress the electromagnet coil insulation. The cable resonance may also be an additional source of EMI. EMI can be increased by operating multiple switching amplifiers for multiple coils, especially if the switching amplifiers are synchronized. EMI can also be increased on longer cables due to more resonance and larger emitting length.
One conventional approach to reduce the EMI radiated by the lead wires includes placing the lead wires in one or more shielded cables. While EMI may be reduced by placing the lead wires in a shielded cable, this approach results in additional drawbacks. For example, the cable resonance may be increased due to the added capacitance between the lead wires and ground (shield). In addition, the shielded cable has capacitive coupling to the lead wires, and a slightly inductive return path to ground. As a result, the shield tends to pick voltages from the lead wires, especially when switching is synchronized, and especially at locations far away from where the shield is tied to ground, both at harmonics of the switching frequency and at the cable resonant frequency. Thus even a shielded cable may be a source of radiated EMI.
What is needed, then, is a switching amplifier capable of supplying voltages to magnetic bearings while reducing EMI caused by switching voltages and cable resonances.